just one question: Is it possible, that the touch keyboard pops up automatically when using the internet explorer in desktop mode just like when using the "tablet mode"? I find it kind of annoying to always push the keyboad button..

Although there's no way to do this, you can map a custom gesture to show the keyboard to make your life a little easier.
Try downloading TouchMe Gesture Studio from the Store. You can use it to configure custom swipe gestures to navigate back/forward, switch tabs, etc...